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12
Argument Filtering Transformation
 In Proc. 1st PPDP, LNCS 1702
, 1999
"... To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this paper, we show that the argument lter ..."
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Cited by 42 (2 self)
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To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this paper, we show that the argument ltering method combining with the dependency pair technique is essential in all the above elimination methods. We present remarkable simple proofs for the soundness of these elimination methods based on this observation. Moreover, we propose a new elimination method, called the argument ltering transformation, which is not only more powerful than all the other elimination methods but also especially useful to make clear the essential relation hidden behind these methods.
Strong Normalisation in the πCalculus
, 2001
"... We introduce a typed πcalculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging namepassing interactive b ..."
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Cited by 32 (17 self)
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We introduce a typed πcalculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging namepassing interactive behaviour. The proof of strong normalisability combines methods from typed lcalculi and linear logic with processtheoretic reasoning. It is adaptable to systems involving state and other extensions. Strong normalisation is shown to have significant consequences, including finite axiomatisation of weak bisimilarity, a fully abstract embedding of the simplytyped lcalculus with products and sums and basic liveness in interaction.
Simple Termination of Rewrite Systems
 Theoretical Computer Science
, 1997
"... In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different defini ..."
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Cited by 17 (2 self)
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In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different definitions are given: one based on (strict) partial orders and another one based on preorders (or quasiorders). We argue that there is no reason to choose the second one, while the first one has certain advantages. Simplification orders are known to be wellfounded orders on terms over a finite signature. This important result no longer holds if we consider infinite signatures. Nevertheless, wellknown simplification orders like the recursive path order are also wellfounded on terms over infinite signatures, provided the underlying precedence is wellfounded. We propose a new definition of simplification order, which coincides with the old one (based on partial orders) in case of finite signatu...
Higherdimensional categories with finite derivation type
"... We study convergent (terminating and confluent) presentations of ncategories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for ncategories, generalising the one introduced by Squier for word rewriting systems. We characterise this pr ..."
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Cited by 13 (3 self)
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We study convergent (terminating and confluent) presentations of ncategories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for ncategories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions for an ncategory to have finite derivation type. Through examples, we present several techniques based on derivations of 2categories to study convergent presentations by 3polygraphs.
Modularity of Confluence: A Simplified Proof
, 1994
"... In this note we present a simple proof of a result of Toyama which states that the disjoint union of confluent term rewriting systems is confluent. 1985 Mathematics Subject Classification: 68Q50 1987 CR Categories: F.4.2 Key Words and Phrases: theory of computation, term rewriting systems, modular ..."
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Cited by 12 (5 self)
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In this note we present a simple proof of a result of Toyama which states that the disjoint union of confluent term rewriting systems is confluent. 1985 Mathematics Subject Classification: 68Q50 1987 CR Categories: F.4.2 Key Words and Phrases: theory of computation, term rewriting systems, modularity, confluence Introduction The topic of modularity of properties of term rewriting systems has caught much attention recently. An introduction to this area can be found in Klop [6]. For an early survey one may consult Middeldorp [7]. Moreover, the topic has received a fruitful offspring in the study of the conservation of properties when adding algebraic rewrite rules to various (typed) lambda calculi, see e.g. BreazuTannen and Gallier [1, 2] and Jouannaud and Okada [5]. 5 Partially supported by ESPRIT Basic Research Action 3020, INTEGRATION. 6 Partially supported by ESPRIT Basic Research Action 3074, SEMAGRAPH. 7 Partially supported by grants from NWO, Vrije Universiteit Amsterdam...
Modeling methods for web application verification and testing: State of the art
, 2008
"... Models are considered an essential step in capturing different system behaviors and simplifying the analysis required to check or improve the quality of software. Verification and testing of web software requires effective modeling techniques that address the specific challenges of web applications. ..."
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Cited by 7 (3 self)
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Models are considered an essential step in capturing different system behaviors and simplifying the analysis required to check or improve the quality of software. Verification and testing of web software requires effective modeling techniques that address the specific challenges of web applications. In this study we survey 24 different modeling methods used in website verification and testing. Based on a short catalogue of desirable properties of web applications that require analysis, two different views of the methods are presented: a general categorization by modeling level, and a detailed comparison based on property coverage.
Termination, ACTermination and Dependency Pairs of Term Rewriting Systems
 Ph.D. thesis, JAIST
, 2000
"... Copyright c ○ 2000 by Keiichirou KUSAKARI Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to ACTRSs, and introduce new methods for eff ..."
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Cited by 5 (0 self)
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Copyright c ○ 2000 by Keiichirou KUSAKARI Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to ACTRSs, and introduce new methods for effectively proving ACtermination. Since it is impossible to directly apply the notion of dependency pairs to ACTRSs, we introduce the head parts in terms and show an analogy between the root positions in infinite reduction sequences by TRSs and the head positions in those by ACTRSs. Indeed, this analogy is essential for the extension of dependency pairs to ACTRSs. Based on this analogy, we define ACdependency pairs. To simplify the task of proving termination and ACtermination, several elimination transformations such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this thesis, we show that the argument filtering method combined with the ACdependency pair technique is essential in all the elimination transformations above. We present remarkable simple proofs for the soundness of these elimination transformations based on this observation. Moreover, we propose a new elimination transformation, called the argument filtering transformation, which is not only more powerful than all the other elimination transformations but also especially useful to make clear an essential relationship among them.
Describing systems of processes by means of highlevel replacement
 IN EHRIG ET AL
"... Graphs and graph transformations are natural means to describe systems of processes. Graphs represent structure of the system, and graph rewriting rules model dynamic behaviour. In this chapter, we illustrate the technique by describing Petri nets, statecharts, parallel logic programming, and system ..."
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Cited by 2 (0 self)
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Graphs and graph transformations are natural means to describe systems of processes. Graphs represent structure of the system, and graph rewriting rules model dynamic behaviour. In this chapter, we illustrate the technique by describing Petri nets, statecharts, parallel logic programming, and systems of processes. Whereas description of Petri nets is based on usual graphs, statecharts lead us to hierarchical graphs, and parallel logic programming needs jungles. Finally, we combine different approaches to describe systems of processes. Topological structure is represented by a hypergraph. Local states and communication channels correspond to nodes that are labelled with parts of a global jungle playing the role of a shared data structure. The formal model takes advantage of commacategory approach allowing to change both the structure of graph and the contents of nodes consistently and to treat different graph structures as well as different labelling mechanisms in
Aart Middeldorp
"... In this paper we investigate the concept of simple termination. A term rewriting system (TRS for short) is called simply terminating if its termination can be proved by means of a simplification order. We propose a new definition of simplification order and we investigate the properties of the resul ..."
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In this paper we investigate the concept of simple termination. A term rewriting system (TRS for short) is called simply terminating if its termination can be proved by means of a simplification order. We propose a new definition of simplification order and we investigate the properties of the resulting class of simply terminating systems. 1. Preliminaries We assume the reader’s familiarity with term rewriting [3, 5]. A binary relation R on terms is closed under contexts if C[s] R C[t] whenever s R t, for all contexts C. We say that R is closed under substitutions if sσ R tσ whenever s R t, for all substitutions σ. A rewrite relation is a binary relation on terms that is closed under contexts and substitutions. A rewrite relation that is also a (strict) partial order is called a rewrite order. A wellfounded rewrite order is called a reduction order. We say that a TRS (F, R) and a partial order ≻ on T (F, V) are compatible if R is contained in ≻, i.e., l ≻ r for every rewrite rule l → r of R. It is easy to show that a TRS is terminating if and only if it is compatible with a reduction order. The subterm relation is denoted by �. We say that a binary relation R on terms has the subterm property if C[t] R t for all contexts C � = � and terms t, i.e., if ⊲ ⊆ R. The subterm property is closely related to embedding. Let F be a signature. The TRS Emb (F) consists of all rewrite rules f(x1,..., xn) → xi with f ∈ F a function symbol of arity n � 1 and i ∈ {1,..., n}. Here x1,..., xn are pairwise different variables. We abbreviate → + Emb (F) to ⊲emb. It is easy to prove that a rewrite order has the subterm property if and only if it is compatible with Emb (F). As a consequence, ⊲emb is the smallest rewrite order 1 with the subterm property. Embedding is a special case of homeomorphic embedding. Let ≻ be a partial order on a signature F. The TRS Emb (F, ≻) consists of all rewrite rules of Emb (F) together with all rewrite rules f(x1,..., xn) → g(xi1,..., xim) with f an nary function symbol in F, g an mary function symbol in F, n � m � 0, f ≻ g, and 1 � i1 < · · · < im � n whenever m � 1. We abbreviate → + Emb (F,≻) to
Approximations for Strategies and Termination Abstract
"... The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing ..."
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The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems. However, needed redexes are not computable in general. In the paper we illustrate, based on the framework introduced in [6], how the use of approximations and their associated tree automata results allows one to obtain decidable conditions in a simple and elegant way. We further show how the very same ideas can be used to improve [18] the dependency pair method of Arts and Giesl [1] for proving termination of rewrite systems automatically. More precisely, we show how approximations and tree automata techniques provide a better estimation of the dependency graph. This graph determines the ordering constraints that have to be solved in order to conclude termination. Furthermore, we present a new estimation of the dependency graph that does not rely on computationally expensive tree automata techniques. 1